Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Jakarta to Missouri as you normally would.
Jakarta Soekarno-Hatta Intl Airport is CGK and Kansas City Airport is MCI. These codes are created by the International Air Transport Association (IATA) and airlines use them to identify the departing and arrival airports in the flight routes they service. Lambert-St Louis Airport (STL), Springfield-Branson Airport (SGF), Columbia Regional Airport (COU), Kansas City Downtown Airport (MKC), Branson Airport (BKG) are some additional IATA codes for airports related to your trip.